A Closer Look at PKI: Security and Eﬃciency

A Closer Look at PKI: Security and Efficiency Alexandra Boldyreva1 and Marc Fischlin2 and Adriana Palacio3 and Bogdan Warinschi4 1Georgia Institute of Technology, USA. [email protected] 2Darmstadt University of Technology, Germany. [email protected] 3Bowdoin College, USA. [email protected] 4University of Bristol, UK. [email protected] April 13, 2007 Abstract In this paper we take a closer look at the security and efficiency of public-key encryption and signature schemes in public-key infrastructures (PKI). Unlike traditional analyses which assume an “ideal” implementation of the PKI, we focus on the security of joint constructions that consider the certification authority (CA) and the users, and include a key-registration protocol and the algorithms of an encryption or a signature scheme. We therefore consider significantly broader adversarial capabilities. Our analysis clarifies and validates several crucial aspects such as the amount of trust put in the CA, the necessity and specifics of proofs of possession of secret keys, and the security of the basic primitives in this more complex setting. We also provide constructions for encryption and signature schemes that provably satisfy our strong security definitions and are more efficient than the corresponding traditional constructions that assume a digital certificate issued by the CA must be verified whenever a public key is used. Our results address some important aspects for the design and standardization of PKIs, as targeted for example in the standards project ANSI X9.109. 1 Introduction Public key cryptography implicitly relies on the existence of a public-key infrastructure (PKI), where each user has a pair of public and secret keys for the cryptosystem, and that this association is publicly available. The designers of public-key cryptosystems always define how the public and the secret keys are generated and used, but almost never carefully specify how the binding between keys and user identities takes place. The tacit assumption is that this binding is established a priori through PKI management operations. 1.1 Motivation The policies and the procedures regarding PKIs are continuously changing and detailed descriptions are invari- ably long and tedious.1 Unfortunately, existing literature still does not answer several important questions. 1See for example the document that describe the current state-of-the-art: ”Internet X.509 Public Key Infrastructure – Cer- tificate Management Protocol (CMP)” [1]. What exactly is the certification authority (CA), the entity that links public keys to identities, trusted not to do? Can and should some degree of security be ensured even when the CA is malicious or becomes compromised? Proofs of possession (POP) —in which a user proves possession of the secret key when registering a public key with the CA— are a defense mechanism for protecting against rogue-key and key-substitution attacks, but what exactly should they be and, more importantly, are they really necessary? A question that is perhaps even more important is whether provably-secure encryption and signature schemes are indeed secure when used in a particular PKI. Although it is largely believed to be the case, the question is far from moot since most existing schemes are analyzed in settings where compositional aspects are neglected. In particular, the security of the combination of a key-registration protocol with existing encryption or signature schemes does not immediately follow from the security of the individual components. In principle, by cleverly combining its ability to attack the key-registration protocol and its ability to attack the primitive (encryption or signatures), an adversary could mount a successful attack against the joint construction. Limitations of security analyses that do not explicitly include the behavior of the CA or the key-registration protocol have been previously pointed out in other contexts. In the case of key exchange, Shoup [40] suggests that registration of public keys should be considered explicitly as part of the key agreement protocol to be analyzed. Kaliski [26] exemplifies the importance of such measures by presenting unknown key-share attacks on the MQV key exchange protocol [33]. These attacks could have been discovered with a thorough analysis that considers the CA as an active party participating in the protocol. We review further related work at the end in Section 6. 1.2 Contributions In this paper we initiate a study of PKIs with respect to security of the two most important public-key primitives: encryption and digital signature schemes. Our main motivation is to answer the questions raised above and other related issues. Models. Security arguments in the absence of rigorous models do not provide strong security guarantees, and such models are conspicuously absent in the case of PKIs. Our first contribution are rigorous definitions for primitives when used in this setting together with appropriate security notions. The inherent complexity of the PKI settings, the non-typical adversarial powers, and the difficulty of precisely identifying the situations that constitute a security breach make the design of such models an entirely non-trivial task. Since security goals depend on the primitive used, we treat the cases in which keys are used for encryption and for signing separately. Specifically, we define two primitives, called certified encryption and certified signature schemes, and for each primitive we define a notion of security. Besides the standard algorithms for encryption and signing, we model explicitly interactive protocols for registering the public keys with a CA. Consequently, our security notions are against an adversary with broad capabilities that take into account threats arising from the key-registration protocol, possibly run concurrently, the presence of several parties, including the users and the (possibly corrupt) CA. The details are in Sections 2, 3 and 4. Our security definitions are general and powerful. The models we propose directly capture settings where users have multiple public keys, and where keys have additional attributes, such as an expiration date. They easily extend to handle hierarchical certification and certificate revocation. Moreover, while we capture the original goal for which PKI was invented we make flexible assumptions on how certification is achieved. In particular, schemes that aim at achieving certification but avoid the original mechanism of explicit certificates specific to the traditional PKIs (e.g. schemes similar to those in [20, 2]) can still be analyzed in our models. We provide a detailed discussion in Sections 3 and 4. The design of our models in general and that of the security goals in particular are motivated by the “core” properties of the primitives, namely, confidentiality for encryption and integrity and authenticity for signatures. For protocols in which encryption schemes or signatures are used beyond these basic properties, e.g., encryption schemes used as commitments, additional analysis in light of the new goals is required. Yet, our attack model should be easily transferable to those scenarios, and only the security definitions would need to be adapted. Analysis of Traditional Schemes. Next we focus on constructions that satisfy the proposed notions of security. We start with an analysis of “traditional” certified encryption and certified signature schemes. In these constructions, the CA uses a signature scheme to issue digital certificates, and then parties produce 2 ciphertexts (resp., signatures) using a standard encryption (resp., signature) scheme. These schemes are defined in detail in Sections 3 and 4, respectively. Although it seems folklore that the traditional approach is “secure”, to the best of our knowledge no formal validation in a sound model with respect to clearly expressed security goals has been devised prior to our work. We offer a rigorous analysis that shows that these schemes are indeed secure in the appropriate security model we design. Our proof gives concrete security bounds that support recommendations for practical parameter choices. While expected, these results are important to increase confidence in the use of the schemes and allow to make security statements based on solid foundations. Our concrete security results are in Sections 3 and 4. The results that we obtain regarding the design of proofs of possession are less expected, if not surprising. Our investigation shows that formal proofs of knowledge are not necessary for basic security of the certified encryption and signature schemes, and that simpler challenge-response protocols suffice. For signatures, the user simply signs a distinct message2 provided by the CA. Perhaps surprisingly, we show that for basic encryption no proof of possession is required. Intuitively, in the case of encryption, this means that data privacy is not compromised if a user does not have the secret key associated to the public key it registers. We note that these results do not eliminate the proof-of-knowledge requirements imposed on these primitives in other settings (e.g., [4, 10, 9, 23, 31, 35]) and only concern the security of certified encryption and signatures. More efficient constructions. Since our models do not require that solutions use explicit certificates as in the traditional constructions, it is natural to ask if it is possible to obtain improvements over the traditional solutions, e.g., in terms of efficiency. We answer this question affirmatively. We present more efficient constructions for certified encryption

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